Federated edge learning (FEL) has recently attracted great interest due to its real-time response and energy-efficient characteristics. Most existing work focuses on designing algorithms to improve model performance, ignoring the malicious behavior and personal decision-making of self-interested edge servers. Although some efforts have been devoted to incentivizing honest edge server engagement by compensating training costs, this rarely considers resource efficiency and often assumes that edge servers provide complete information to the platform, which may lead to the risk of private attribute leakage. Hence, we aim to achieve an incentive mechanism that promotes secure and efficient model training between the platform and edge servers. However, edge servers’ multi-dimensional private attributes and training strategies make the optimization problem nonconvex, and incomplete information further increases the complexity of the analysis. In order to address these challenges and by integrating contract theory and exponential mechanism, we propose an efficiency-aware incentive mechanism, FedNow, which enables edge servers to personally determine their local training rounds while motivating their participation without giving access to their true training strategies and private attributes. Specifically, we enabld edge servers to add noise to their submitted training strategy to hide their true training rounds; then, we carefully designed an efficiency score function to select honest and efficient edge servers without disclosing their private attributes. In order to demonstrate that FedNow strictly outperforms existing schemes in terms of total costs, we theoretically derived sufficient conditions for making the total costs of FedNow lower than existing schemes and designed a greedy algorithm that uses the Monte Carlo method to find feasible near-optimal solutions in polynomial time. Our extensive experimental assessment using synthetic and real datasets shows the superiority of FedNow.